Tim has just inherited £1000 and he decides not to invest it but rather to spend 10% of the remaining money each month. Each month Tim's saving thus reduce by a factor of 0.9 Calculate, to the nearest integer, the amount remaining (in E) after 20 months. You may find it useful to first devise a formula for the amount remaining after n months. Enter your answer, to the nearest integer and without units, in the box below. Answer:

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pandeyarindam296 pandeyarindam296 · Answer 1 · 2019-09-18T15:00:16+02:00

Answer:

£ 121.57

Step-by-step explanation:

As given in question,

Total amount inherited by Tim = £1000

He spends each month = 10 % of remaining money

savings reduced each month = 0.9 of remaining amount

So, the amount of money after one month = 0.9 x £1000

amount of money remained after 2 months = 0.9 x 0.9 x £1000

amount of money remained after 3 months = 0.9 x 0.9 x 0.9 x £1000

Hence, the amount of money remained after the n months can be given by,

[tex]E\ =\ 0.9^n\times 1000[/tex]

Hence, amount of money remained after 20 months can be given by,

[tex]E_{20}\ =\ 0.9^{20}\times1000[/tex]

= £ 121.57

So, the amount of money remained after 20 months will be £ 121.57.